day 1

day 2

### 4.3 investigating transformations

By the end of these lessons you will be able to:

- describe transformations of parabolas in vertex form

- write the equation of a parabola in vertex form

- identify the vertex, axis of symmetry, and the maximum or minimum point

### Day 2 video tutorial: Describing transformations (part 2)

Ontario Curriculum

Overall Expectations:

• determine the basic properties of quadratic relations;

• relate transformations of the graph of y = x2 to the algebraic representation   y = a(x – h)2 + k;

• solve problems involving quadratic relations.

Specific Expectations:

- identify the key features of a graph of a parabola (i.e., the equation of the axis of symmetry, the coordinates of the vertex, the y-intercept, the zeros, and the maximum or minimum value)

- identify, through investigation using technology, the effect on the graph of y = x2 of transformations (i.e., translations, reflections in the x-axis, vertical stretches or compressions) by considering separately each parameter a, h, and k

- explain the roles of a, h, and k in y = a(x – h )2 + k, using the appropriate terminology to describe the transformations, and identify the vertex and the equation of the axis of symmetry;

- sketch, by hand, the graph of y = a(x – h )2 + k by applying  Transformations to the graph of y = x2